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In this paper we introduce a natural definition for the affine maps betweentwo Finsler manifolds $(M, F)$ and $(N,\tilde F)$ and we give some geometricalproperties of these affine maps. Starting from the equations of the affinemaps, we construct a natural Berwald-Riemann-Lagrange geometry on the 1-jetspace $J^1(TM;N)$, in the sense of a Berwald nonlinear connection$\Gamma^b_jet$, a Berwald $\Gamma^b_jet$-linear d-connection $B\Gamma^b_jet$,together with its d-torsions and d-curvatures, which geometricallycharacterizes the initial affine maps between Finsler manifolds.

Jet Berwald-Riemann-Lagrange Geometrization for Affine Maps between Finsler Manifolds